71.3.16 problem 11

Internal problem ID [14295]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 11
Date solved : Monday, March 31, 2025 at 12:15:57 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-3 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(y(x),x) = y(x)^2-3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{1+3 \,{\mathrm e}^{3 x} c_1} \]

✓ Mathematica. Time used: 0.224 (sec). Leaf size: 40

ode=D[y[x],x]==y[x]^2-3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-3) K[1]}dK[1]\&\right ][x+c_1] \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}

✓ Sympy. Time used: 0.324 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 + 3*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 C_{1}}{C_{1} - e^{3 x}} \]